Interest-Only Mortgages and Consumption Growth: Evidence from a Mortgage Market Reform - Department of ...
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Interest-Only Mortgages and Consumption Growth:
Evidence from a Mortgage Market Reform
Claes Bäckman and Natalia Khorunzhina∗
January 17, 2019
Abstract
We use detailed household-level data from Denmark to analyze how the
introduction of interest-only mortgages affected consumption expenditure and
borrowing. Four years after the reform interest-only mortgages constituted 40
percent of outstanding mortgage debt, making up more than half of mortgage
debt for borrowers in the top and bottom decile of the income. Using an ex-ante
measure of exposure motivated by financial constraints, we show that households
more likely to use an IO mortgage increased their consumption substantially fol-
lowing the reform. The increase in consumption is driven by higher borrowing at
the time of refinancing and by borrowers with lower pre-reform leverage ratios.
Housing wealth effects and labor market dynamics are unlikely to explain the
results.
JEL Classification: D14, E21, G21, R21, R30 ;
∗
Bäckman: Department of Economics and Knut Wiksell Centre for Financial Studies, Lund Uni-
versity, Tycho Brahes väg 1, 223 63 Lund, Sweden. Email: claes.backman@nek.lu.se. Khorunzhina:
Copenhagen Business School, Department of Economics. Porcelœnshaven 16a, 2000 Frederiksberg,
Denmark. Email: nk.eco@cbs.dk. We would like to thank Marcus Asplund, João Cocco, Fane Groes,
Søren Leth-Petersen, Sumit Agarwal, Irina Dyshko and seminar participants at Riksbanken and
Aarhus University for helpful comments.1 Introduction
Four year after a 2003 mortgage market reform that introduced interest-only mort-
gages in Denmark, these new mortgage products made up close to 50 percent of out-
standing mortgage debt and aggregate mortgage debt had increased by 40 percent.
This mortgage credit expansion occurred proportionally across the income and wealth
distribution, was associated with a decline in leverage and was followed by a rapid
increase in house prices. House price growth had trended downwards prior to the
reform, but started accelerating once mortgage banks were allowed to sell the new
products. Quantitatively, Denmark experienced a similar increase in household debt
as the United States over the same time period, even as the regulatory loan-to-value
ratio was unchanged, sub-prime borrowing was nonexistent and there was no increase
in securitization.1
How can we explain these developments? The explanatory power of several expla-
nations for the rise in US debt and defaults is limited by the Danish institutional
framework, as Danish mortgage banks are strictly regulated in their ability to extend
credit to sub-prime borrowers or to increase securitization, and Danish borrowers face
full recourse on their debt and thus have incentives not to unduly speculate on rising
house prices. Moreover, the impact of interest-only mortgages is difficult to recon-
cile with traditional models where borrowing is based on collateral constraints for a
simple reason: amortization payments do not constrain borrowing in these models
(see Guerrieri and Uhlig, 2016, for an overview of collateral-based models).2 This
modeling approach to credit constraints is also difficult to reconcile with the facts,
as the regulatory loan to value ratios in Denmark were constant and aggregate lever-
age declined (Justiniano et al., 2018, reports similar statistics for the United States).
Recent macroeconomic models that incorporate payment-to-income (PTI) constraints
1
In the United States, interest-only mortgages and similar unconventional products accounted for
approximately 50 percent of mortgage origination in 2007, having increased from one percent in 2000
(Justiniano et al., 2017). See also Barlevy and Fisher (2011) and Dokko et al. (2015).
2
Lower amortization payments could be used to increase consumption smoothing (Cocco, 2013),
which would lead to a rise in debt as households stop paying down their debt . However, we will show
that this effect is not sufficient to explain the increase in borrowing and consumption.
1provide more scope for an effect, as amortization payments directly enter the con-
straint (Grodecka, 2017; Kaplan et al., 2017; Greenwald, 2017). However, it is a-priori
unclear how many households are affected by payment constraints, and indeed also
how changing such constraints affect borrowing and consumption.
In this paper we provide empirical support for the importance of payment-to-income
constraints, and examine how a relaxation of such constraints affect borrowing and
consumption expenditure. Our first contribution is to provide an intuitive and novel
equation for when payments constraints are binding and to test how households re-
sponded to a relaxation of this constraint. For households bound by a PTI constraint,
borrowing is limited by the payments that they have to make to use the collateral.
With both a loan-to-value constraint and a payment constraint, borrowing will be
determined by the lesser of the two constraints and we can write up the condition for
when payments are binding: for a sufficiently high house value to income ratio the
payments on the mortgage constrain borrowing, not the value of the collateral. This
simple prediction fits the data on borrowing well. House value to income ratios strongly
predicts whether households use interest-only mortgages: 62 percent of homeowners in
the top quartile had an IO mortgage, compared to 32 percent in the bottom quartile.3
Amromin et al. (2018) report similar statistics for the United States. Consistent with
an interaction between two binding constraints, leverage is declining in house value to
income ratios and interest-payments to income are increasing.
We estimate the impact of the introduction of interest-only mortgages on consumption
expenditure of existing homeowners using their house value to income ratio measured
prior to the reform as our measure of exposure. Our empirical strategy is similar to
Mian and Sufi (2012) and Berger et al. (2016). An extensive analysis of time-trends
indicates parallel trends in consumption growth prior to the reform across groups with
differing levels of exposure to the reform, followed by a clear break with increasing
consumption growth for groups with high exposure and continued higher consumption
3
This pattern holds after controlling for a wide range of household demographic and financial
characteristics.
2levels. We estimate that one standard deviation higher house value to income is asso-
ciated with an approximately 5 percent increase in consumption growth. In aggregate,
IO mortgages increased consumption by 7.6 percent between 2004 and 2010, corre-
sponding to 52 percent of the total increase in consumption expenditure. We find that
the effect is driven by older households and by households with low ex-ante leverage.
Higher leverage in 2002 is associated with a lower response to interest-only mortgages.
While this is inconsistent with a relaxation of binding collateral constraints, the result
is consistent with binding PTI constraints limiting households ability to access their
collateral.
Household consumption expenditure remains higher even as the housing market cycle
turns and house prices decline by an average of 30 percent. The lack of a reversal
strongly suggests that our results are not driven by housing wealth effects or labor
market dynamics. In addition, the empirical evidence from Denmark suggest that
wealth effects are small. Browning et al. (2013) find very limited evidence for housing
wealth effects during 1987-1996. When we extend their results up until 2010, we find
that the only years when house prices have a significant impact on consumption are
between 2004 and 2006.4 This result is driven by a higher refinancing rates in high
house price growth areas relative to low growth areas. If we control for refinancing,
there is no evidence of a housing wealth effect. Andersen and Leth-Petersen (2018)
find similar results using household-level survey data on house price expectations in
a later period in Denmark. We concur with their assessment that the existence of a
housing wealth effect is intimately linked to the functioning of the mortgage market.
If interest-only mortgages relax borrowing constraint, we expect to see higher borrow-
ing at the time of refinancing (what Greenwald, 2017, calls the “frontloading effect”).
We provide evidence for this effect by exploiting the timing of when the household
chooses to refinance to an IO mortgage (Fadlon et al., 2015; Druedahl and Martinello,
2017). Using year and household fixed effects to address endogeneity concerns related
4
This result holds for any subgroup of the population that we consider, including liquidity con-
strained, borrowing constrained and across age groups.
3to fixed household characteristics and business cycle effects, we compare the behav-
ior of households who chose to refinance to an IO mortgage in different years. The
increase in consumption expenditure is almost entirely driven by higher borrowing at
the time of mortgage refinancing: there is a spike in consumption expenditure at the
time of refinancing, followed by a reversion towards the previous trend. On average
half of the increase in mortgage debt at the time of refinancing goes into consumption
expenditure. We therefore do not find strong evidence for an increase in consumption
expenditure levels due to interest-only mortgages. However, while we find that the
main impact is through higher borrowing at the time of refinancing and not through
lower payments afterwards, an analysis of heterogeneous responses suggest that older
borrowers use the reduction in payments to increase consumption afterwards. This is
consistent with consumption smoothing behavior on behalf of older households, who
after retirement wish to live off their wealth. The consumption smoothing argument
not only applies to young households with rising incomes (Cocco, 2013), but also to
older households who after retirement have income lower than their permanent income.
In essence, the forced savings inherent in amortizing mortgages are a cost for these
households, which can be reduced by choosing an IO mortgage instead.5
These results are similar to the results in the literature that studies the household
response to lower interest payments (Agarwal et al., 2017; Abel and Fuster, 2018).6
Bhutta and Keys (2016) find that interest payments have a substantial impact on
household borrowing, an effect is particularly pronounced among younger borrowers
with prime credit scores. Our results also provide an alternative mechanism for the
higher sensitivity to interest-rates documented by Beraja et al. (2018): borrowers
constrained by mortgage payments are not able to borrow against the value of their
collateral, and therefore end up with higher equity. When the mortgage rate falls
5
Note that this requires that the household face binding credit constraints - households who can
borrow unrestrictedly could undo any amortization payment by either refinancing their mortgage and
increased their debt (Hull, 2017), or could simply borrow more initially and use the additional funds
to amortize (Svensson, 2016).
6
See also Di Maggio et al. (2017), who find that lower mortgage payments substantially increase
consumption and Cloyne et al. (2016), who show that borrowers in the United Kingdom and the
United States increase their spending in response to lower interest payments.
4borrowers are able to take advantage of their collateral, and borrowing increases.
We also contribute to the theoretical macroeconomic literature that tries to explain
the boom and bust in house prices. Within recent models incorporating PTI con-
straints there is disagreement on the impact of credit shocks. Greenwald (2017) shows
that in a model where all agents are homeowners (without a rental market) relaxing
PTI constraints leads to a large increase in debt, house prices and consumption.7 In
contrast, Kaplan et al. (2017) construct a model where households choose whether to
become a homeowner (with a rental market) where credit supply shocks have no im-
pact on house prices or consumption, but have a large impact on the homeownership
rate. They instead argue that house price expectations (beliefs) were the key driver
behind the housing boom and bust. The key differences between Greenwald (2017)
and Kaplan et al. (2017) is the presence of a rental market that can absorb credit
supply shocks. A perfect rental market implies that credit supply shocks move the
homeownership rate, whereas a model where all households are homeowners implies
that the effect will come through prices. While we do not discount the importance of
beliefs for driving house prices, we note that in Denmark the homeownership rate did
not change in response to the introduction of interest-only mortgages (Bäckman and
Lutz, 2018). This provides scope for a response in borrowing and house prices. Indeed,
house prices increased following the introduction of interest-only mortgages (Bäckman
and Lutz, 2018). This also implies that a part of the increase in consumption comes
through a wealth effect. This would still represent a causal impact of the introduction
of IO mortgages on consumption, as any housing wealth effect arises from rising house
prices due to IO mortgage.
The Danish institutional framework for mortgage financing helps rule out several other
confounding factors. Mortgage debt is more strictly regulated in Denmark compared
to the United States, with corresponding incentives for both mortgage banks and
households to not unduly speculate on rising house prices.8 Danish mortgage banks
7
See also Favilukis et al. (2017) and Justiniano et al. (2018).
8
Brueckner et al. (2016) argue that because IO mortgage postpone repayments, the higher risk
of negative equity makes this product riskier. In their model, this risk is mitigated if house price
5are legally required to evaluate the income and house value for each borrower to assess
whether the borrower can repay a standard 30-year fixed rate mortgage product even
in the face of increasing interest rates. This requirement is incentivized through reg-
ulation that mandates that the mortgage banks are liable for any losses incurred on
mortgage bonds by investors, even as those bonds are sold off to investors (Campbell,
2013). Other criteria for mortgage lending did not change during the boom. Mortgage
borrowing was limited to 80 percent of the house value, and borrowers were evaluated
on their ability to afford higher interest payments. Borrowers have a strong incentive
to conform to these limits and not to overextend themselves, as all debt in Denmark
is full recourse (and the laws are enforced). Indeed, there was no default crisis in
Denmark even as housing markets declined by 30 percent - mortgage arrears peaked
at 0.6 percent of outstanding mortgage debt.
Our paper is related to several other studies that examine consumption and borrowing
for Danish households in the period around the financial crisis. Andersen et al. (2016)
study how leverage in 2007 affected consumption growth between 2007 and 2009.
Their conclusion is that the negative relationship between leverage and consumption
is the result of a spending normalization that occurs because highly levered households
borrowed more on the eve of the crisis to fund consumption. Jensen and Johannesen
(2016) find that a credit supply to banks had a strong negative and persistent effect on
the consumption of their borrowers. Kuchler (2015) finds that in 2012 households with
interest-only mortgages in Denmark have lower savings rate and higher loan-to-value
ratios. Finally, in a closely related study, Larsen et al. (2018) study how homeowners
used interest-only mortgages in Denmark using a different dataset and a difference-
in-difference strategy. Overall, their study corroborate our results by showing that
households with interest-only mortgages increase their consumption and have higher
mortgage debt.
In general, this paper illustrates the importance of payment constraints in the mort-
expectations are high. Our focus on existing homeowners and the fact that default is an prohibitively
expensive option in Denmark limit the concern that households are using IO mortgages to speculate.
6gage market and provides evidence on how credit supply shocks affect macroeconomic
outcomes. The results are important not only for diagnosing the boom-bust episodes
in Denmark, the United States and elsewhere, but also for policies that guard against
future crises. In particular, our results suggest a framework for analyzing the impact
of macroprudential policies on the cross-section of households, and suggest that such
policies can have a large impact on borrowing and consumption expenditure.
2 The introduction of interest-only mortgages
Interest-only mortgages were introduced in Denmark in 2003.9 This new product
was introduced through a regulatory reform, as the regulatory framework specifically
details which mortgage products the mortgage banks are allowed to offer their cus-
tomers. The purpose was to increase affordability and flexibility for temporarily credit
constrained households, where the expectation was that this would be a niche product
that would not impact house prices or consumption.10 The legislation that allowed the
mortgage banks to offer interest-only mortgages, in Denmark referred to as a “deferred
amortization” mortgage (afdragsfrie lån), was introduced to the Danish parliament on
March 12, 2003 and was voted through parliament on June 4. Mortgage banks were
allowed to start selling interest-only mortgages in October of 2003. The new product
allowed for a 10 year period without amortization payments, after which the borrower
had to repay the outstanding debt over the remaining life-span of the mortgage.
Importantly, other aspects of the regulatory framework were unchanged.11 There was
9
Technically, a bank customer could approximate an interest-only mortgage prior to the reform by
either continuously refinancing Hull (2017) or by extracting more equity and using excess funds to pay
the amortization payments. The other banking institutions were also allowed to offer interest-only
mortgages to their customers. Consequently, the reform can be seen as allowing for an easier and less
expensive way of taking out such a mortgage product.
10
Additional material on the process, the motivation and the debate surrounding the introduction
of IO loans can be found at https://www.retsinformation.dk/Forms/R0710.aspx?id=91430 and
at http://webarkiv.ft.dk/Samling/20021/MENU/00766131.htm.
11
Danish mortgage credit banks provide mortgage loans to households and sell bonds to investors
using the payments from the mortgage loans. The mortgage system operates according to a “matched
funding” principle, where each mortgage loan is matched by a mortgage bond sold to investors. A
more comprehensive overview can be found in Association of Danish Mortgage Credit Banks (2009),
Danske Bank Markets (2013), Campbell (2013, p. 28) and Kuchler (2015).
7no government intervention in the mortgage market, neither through direct ownership
of mortgage debt nor through government insurance of mortgage debt. Similar to the
United States, the predominant mortgage contract in Denmark has historically been
the 30 year fixed rate mortgage, which made up over 90 percent of outstanding mort-
gages in the early 2000s. This is the longest maturity allowed, and is also the most
popular. Variable-rate mortgage was introduced already in 1997. The interest rate on
mortgages is decided by investors in mortgage bonds, not by the mortgage bank itself.
All borrowers can refinance with no pre-payment penalty, regardless of their equity po-
sition. In other words, there is no lock-in effect of housing equity for mortgage rates.
Households can refinance to extract home equity up to the maximum loan-to-value
limit of 80 percent. This requirement was enforced throughout our sample period for
all types of mortgages (Ministry of Economic and Business Affairs, 2007). The cost
for refinancing is approximately 10,000 DKK ($1,500) (Andersen et al., 2015). Bor-
rowers are evaluated on their ability to afford a standard 30-year fixed rate mortgage
regardless of the mortgage contract they choose, and all mortgage debt is full recourse.
In the case of a borrower default, the mortgage bank that supplied the mortgage can
enact a forced sale of the collateralized property. If the proceeds from the sale are
insufficient to cover the outstanding debt, the mortgage bank can garnish the incomes
of the borrower until the debt is repaid. This ensures that there is no strategic incen-
tive to default in Denmark, regardless of the equity position. Indeed, any outstanding
debt will have a higher interest rate than previously.
Due to higher principal debt over the first 10 years, total interest-payments over the
life-span of the loan are higher for an interest-only mortgage compared to a mortgage
that is amortized. The law proposal specifically mandates that the mortgage banks
inform their customers of both the higher costs and the higher risk associated with
these products. In a 2011 survey of IO loan holders, 89 percent reported being “very
well informed” or “well informed” about both the higher cost and the higher risk
associated with their mortgage choice (Association of Danish Mortgage Credit Banks,
2011).
82,000,000 1
Mortgage Debt, Million DKK .9
.8
1,500,000
IO Loan Fraction
.7
.6
1,000,000 .5
55.3 - 68.4
.4
52.6 - 55.3
.3 51.7 - 52.6
500,000
.2 49.0 - 51.7
.1 46.6 - 49.0
0 0 37.0 - 46.6
No data
2000m7
2001m1
2001m7
2002m1
2002m7
2003m1
2003m7
2004m1
2004m7
2005m1
2005m7
2006m1
2006m7
2007m1
2007m7
2008m1
2008m7
2009m1
2009m7
2010m1
2010m7
2011m1
Traditional Mortgage Products Interest-Only Mortgages
IO Mortgage Fraction
Mortgage Debt and IO Mortgage Share over Time
IO Mortgage Share in 2009 Across Municipalities
Figure 1: IO Mortgage Penetration
Notes: The figure plots outstanding mortgage debt in DKK divided into traditional amortizing mortgages and interest-
only mortgages, from Nationalbanken. The grey line plots the fraction of all outstanding interest-only mortgages.
Source: Nationalbanken
In addition, mortgage banks were required to assess the credit risk of the borrower,
and had to maintain all credit risk on their balance sheet. Mortgage credit banks
use the proceeds from their borrowers to issue mortgage-backed bonds to investors.
Mortgage banks receive fees from borrowers but do not receive interest income or
mortgage repayments, which instead accrue to the bond investor. To limit moral
hazard all mortgage credit banks are legally required to retain all credit risk on their
balance sheets. If a borrower defaults, the mortgage bank who issued the bond has to
replace the defaulting mortgage with a bond with equivalent interest rate and maturity.
Investors therefore bear all refinancing and interest-rate risks, but face no credit risk.
This system operates without government intervention or direct guarantees.
Interest-only mortgages rapidly became a popular product. Three years after the re-
form, Figure 1 shows that close to a third of outstanding mortgage debt in Denmark
was held in interest-only mortgages. IO mortgages remain a popular product even
after the financial crisis, representing approximately 50 percent of outstanding mort-
gage debt in 2011. Moreover, interest-only mortgages are prominently used in areas
with high house price levels such as Copenhagen or the other larger cities, but are
also popular in other areas. When we examine Danish municipalities (approximately
equivalent to a US county) on the right hand side of Figure 1, the lowest penetration
9was 37 percent and the highest one was close to 70 percent. This is somewhat in
contrast to evidence from the United States, where Amromin et al. (2018) and Bar-
levy and Fisher (2011) report that IO mortgages were prominent in areas where house
price growth was high but not elsewhere. The Danish housing decline and following
recession did not reduce the popularity of these products, in contrast to how the use of
similar products evolved in other countries. Barlevy and Fisher (2011) and Amromin
et al. (2018) find that IO mortgages in the United States essentially disappeared after
the housing crash and Cocco (2013) documents that IO mortgages in the UK became
less prominent after a regulatory change in 2000. Even though Danish house prices de-
clined by a similar magnitude as in the United States, these products remain popular
and in use today.
3 Data, Variables and Imputing consumption
Denmark Statistics provides data on wealth, income, and demographic characteristics
for the full population of Denmark. This data is collected through third-party report-
ing and is highly reliable, accurate and comprehensive. We use this data to construct a
panel of individuals which includes information on demographics such as age, gender,
education, marital status, the number of children, and municipality of residence; dis-
aggregated asset and debt information such as stock and bond holdings, cash deposits
at banks, bank debt and the market value of mortgage debt; labor market information
such disposable income, wages and employment status; housing information includ-
ing ownership status, property values, number of properties, and any housing market
transactions.
We add more detailed information about mortgage debt characteristics to this dataset.
Mortgage data is provided annually by Finance Denmark starting in 2009, and contains
information from the 5 largest mortgage banks in Denmark with a total market share
12
of more than 90 percent. We use the origination date to assign the mortgage back to
12
See Andersen et al. (2015) for more information about the registry.
10the years before 2009. Specifically, we aggregate loan values and other characteristics
based on the origination year of the mortgage, and then merge these characteristics to
individuals prior to 2009.13
For each mortgage we observe loan size, bond value, maturity, the origination date of
the mortgage, whether it is an interest-only loan and whether the mortgage has a fixed
interest rate. We also observe a unique loan number, which can be shared between
several individuals. As we observe the total loan size and not the individual’s share
of the mortgage, we calculate a equal weight based on the number of individuals with
the same loan number. For example, if a mortgage loan occurs twice in the data, we
assign half the loan value to each individual.
As we will show later, a crucial variable for our analysis is the house value to income
ratio. We construct this variable for each individual using adjusted tax assessed house
values divided by disposable income. Tax assessed house values in the administrative
data systematically underestimates actual house values, and we therefore adjust them
using a scaling factor. The scaling factor is constructed as the ratio between the actual
sales price and the tax assessed valuation for all housing transaction in a given year.
We then average the scaling factor for each year-municipality cell and multiply the tax
assessed values for each individual based on the municipality they live in.14 Finally,
we divide this measure by disposable income to attain a House Value to Income ratio.
We construct two variables related to credit constraints. First, we measure liquidity
constraints as the sum of stocks, bonds and cash deposits divided by disposable income.
We create a dummy equal to one if liquid assets are less than 1.5 months of income
(Browning et al., 2013). Second, we measure collateral constraints as the value of
outstanding mortgage debt divided by housing wealth, which we refer to as leverage,
or loan-to-value (LTV). We create a dummy equal to one if the LTV ratio is above
13
With this procedure, we are unable to classify whether a mortgage is interest-only or not in the
years prior to the most recent refinancing. In effect, the match is worse the further back in time we
go, as households refinance to take advantage of lower interest rates.
14
Denmark Statistics calculates the equivalent scaling factor, but we are unable to use theirs because
of the municipality reform in 2007. For the years when we can compare our scaling factor to the one
provided by Denmark statistics, the two are consistent.
110.5, and also create deciles of leverage.
Our key outcome variable is consumption expenditure. We impute it based on infor-
mation on income and changes in wealth. By definition, spending in a given year is
equal to disposable income minus the increase in net wealth. Since we observe these
variables, we can compute consumption expenditure for individual i at time t as:
Consumption Expenditureit = disposable incomeit − (net wealthit − net wealthit−1 )
This procedure has been used in numerous empirical studies using Danish data (see
e.g. Leth-Petersen, 2010; Browning et al., 2013; De Giorgi et al., 2016; Jensen and
Johannesen, 2016). More importantly, imputed consumption expenditure has been
validated by comparing it to survey measures, and has generally performed well on
average (Browning and Leth-Petersen, 2003; Kreiner et al., 2015).15 Jensen and Jo-
hannesen (2016) compare an aggregated measure of imputed consumption in Danish
registry data to the value of private consumption in the national accounts, and shows
that the trend in these two measures is very similar from 2003 to 2011.
The main concern with imputed consumption is that changes in the valuation of items
on the balance sheet will be measured as consumption. For example, unrealized capital
gains on stock portfolio will be measured as consumption. Similarly, an increase in
the interest rate will lead to a decrease in the market value of a fixed rate mortgage,
increasing net wealth and lowering consumption expenditure. This is not an issue for
housing, where we can observe all property transactions. Since we are not interested
in households who do trade housing, we remove them from the sample and do not
include changes in housing wealth in the imputation.
Browning and Leth-Petersen (2003) find that imputed consumption corresponds well to
the self-reported consumption on average, but that outlier values can be problematic.16
15
See also Koijen et al. (2015) for a similar procedure using Swedish data, and Ziliak (1998), Cooper
(2013) and Khorunzhina (2013) for imputed consumption using survey data.
16
Koijen et al. (2015) point to a similar issue for imputed consumption in Swedish administrative
data.
12We winsorize consumption expenditure at the 1st and 99th percentile. Finally, we limit
the sample to individuals who are present during all relevant years (from 2000 to 2010,
a total of 11 periods).
To address concerns over the stock portfolio (Koijen et al., 2015), we approximate
capital gains on stock portfolios with the market portfolio return. Specifically, we
multiply the value of stock holdings at the beginning of the year with the over-the-
year growth in the Copenhagen Stock Exchange (OMX) C20 index, and calculate
active savings as the end-of-year holdings minus stock holdings at the beginning of the
year adjusted for the capital-gains.
Table 1 provides summary statistics by mortgage type using data from 2002. Con-
sumption in both levels and as a share of disposable income is higher for households
with an IO mortgage, a first piece of evidence that IO mortgage holders may be
more constrained. Consistent with higher constraints, we find higher mortgage to in-
come, interest-payments to income and a larger share facing liquidity and borrowing
constraints among households with an IO mortgage. Second, IO mortgage holders ex-
perienced lower income growth and higher house price growth over the housing market
boom period.
The use of the new mortgage product is not concentrated only among low-income
borrowers. Figure 2 shows that, conditional on holding mortgage debt, IO mortgages
proved popular throughout the (a) age, (b) income, and (c) wealth distributions. All
plots are calculated for the year of origination. The IO mortgage share is U-shaped
in the income and wealth distribution, where both the lower and upper ends of the
distribution are more likely to hold an IO mortgage. This suggests that IO mortgages
provide a credit supply shock that affected both high and low income households This is
in line with the findings in Amromin et al. (2018), who argue that in the United States
similar products were primarily used by sophisticated and high-income borrowers with
high credit scores.
The interest-only mortgage share is strongly increasing in mortgage size. Panel (d)
13Table 1: Summary Statistics by Mortgage Choice
IO Mortgage Traditional Mortgage Difference Highest-Lowest
Financial Characteristics
Consumption 210,198 198,014 -12,183***
(132,999) (113,782) [-30]
Disposable Income 199,436 197,941 -1,495***
(93,411) (68,902) [-6]
Mortgage Debt 549,233 447,546 -101,687***
(303,964) (247,147) [-112]
House Value 995,969 854,118 -141,851***
(581,080) (477,178) [-82]
Sum of Liquid Assets 58,995 63,134 4,140***
(173,271) (177,358) [7]
Interest Payments 42,337 35,724 -6,612***
(22,322) (18,102) [-100]
Consumption to Income 1.06 1.01 -0.06***
(0.51) (0.44) [-35.08]
Consumption growth 2002-2006 0.14 0.09 -0.05***
(0.63) (0.57) [-26.63]
House Value to Income 5.14 4.39 -0.75***
(2.65) (2.14) [-94.96]
House Price Growth 2003-2006 40.26 36.25 -4.01***
(14.92) (15.10) [-80.34]
Income growth 2002-2006 -0.00 0.04 0.04***
(0.30) (0.25) [49.44]
Liquid Assets to Income 0.28 0.30 0.02***
(0.58) (0.53) [10.59]
Mortgage to Income 2.61 2.31 -0.30*
(61.37) (5.80) [-2.25]
Mortgage Rate 0.06 0.07 0.00***
(0.02) (0.03) [58.58]
Interest Payments to Income 0.16 0.13 -0.02***
(0.08) (0.07) [-94.36]
Liquidity Constrained 0.55 0.49 -0.07***
(0.50) (0.50) [-40.95]
Borrowing Constrained 0.76 0.71 -0.05***
(0.43) (0.46) [-33.23]
Household Demographic Characteristics
Age 45.85 43.75 -2.10***
(10.43) (9.01) [-65.66]
Education Length 13.63 13.72 0.09***
(2.66) (2.58) [10.62]
Family Size 3.02 3.12 0.10***
(1.22) (1.19) [24.75]
Employment Ratio during the Year 0.97 0.97 0.00***
(0.12) (0.11) [6.91]
Observations 155923 216261 372184
Notes: Descriptive statistics by mortgage choice for 2002. Column 1 includes all individuals who had an
IO mortgage in 2009, and Column 2 includes all individuals who had a traditional, amortizing mortgage
in 2009. Column 3 reports the differences between column 1 and 2, including the results from a T-test for
differences. For each individual we report demographic and financial characteristics. Financial characteristics
include consumption (defined in section 3), disposable income (the sum of income minus taxes, transfers and
interest-payments), mortgage debt as the market value of outstanding mortgage debt, house value as the tax
assessed value of all housing properties multiplied by the scaling factor, liquid assets as the sum of stocks,
bonds and cash deposits holdings, interest payments as the sum of mortgage and bank deb interest payments.
Mortgage rate is the sum of mortgage interest payments divided by the market value of the mortgage. All
variables marked as ”to Income” is the variable itself divided by disposable income. House price growth
is defined as the percentage growth in square meter prices from 2003 to 2006. Personal income growth is
the percentage growth in personal income (defined as the total income that the individual receives from all
sources). Liquidity constrained is a dummy equal to one if liquid assets are less than 1.5 months of income,
and borrowing constrained is a dummy equal to one if mortgage value divided by house value is greater than
0.5. Demographics include age, years of education, family size and the employment ratio during the year.
Standard deviations are in parentheses. ***, **, * denote significance at the 1%, 5%, and 10% for the T-test.
14Figure 2: IO Mortgage Penetration
1 1
.9 .9
.8 .8
.7 .7
IO Loan Share
IO Loan Share
.6 .6
.5 .5
.4 .4
.3 .3
.2 .2
.1 .1
0 0
20 25 30 35 40 45 50 55 60 65 70 75 80 1 2 3 4 5 6 7 8 9 10
Age Income Distribution
(a) IO Mortgages by Age (b) IO Mortgages by Income
1 .7
.9
.6
.8
Share of IO Loans
Share of IO Loans
.7
.5
.6
.5
.4
.4
.3 .3
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
Decile Based on Total Wealth Decile Based on Initial Mortgage Size
(c) IO Mortgages by Wealth (d) IO Mortgages by Mortgage Size
Notes: The figure plots the share of mortgage debt that is interest-only. Age, Income, wealth and initial mortgage
size is calculated for the year of origination. All observations are on the individual level. Data on mortgage choice is
originally from 2009, but matched back in time by year of origination. Panel (a) plots the IO share by age, panel (b)
plots the IO share by income deciles, panel (c) plots the IO share by total wealth, and panel (d) plots the IO mortgage
share based on the initial size of the mortgage.
15reports the IO mortgage share by mortgage size at origination. The share is approx-
imately 38 percent in the lowest decile, but increases rapidly as the mortgage size
increases. In the top decile, the share of IO mortgages is over 65 percent. This rela-
tionship also holds when we control for income or other variables.
In Table 2 we report regression results. The dependent variable in all regressions is a
dummy variable equal to one if the individuals holds an IO mortgage, and zero if not.
We focus on the sample where we can identify the type of mortgage the individual
holds. The independent variables are house value to income and loan value to income,
along with a number of demographic controls. We also control for municipality and
year of origination fixed effects. We standardize house value to income and loan value
ratios to income to have zero mean and unit variance, and provide results separately
for fixed (column 3 and 7) and variable rate loans (column 4 and 8).
The coefficient on the House value to income and Loan size to income ratios are all
positive and strongly significant. A one standard deviation increase in loan size to
income increases the share of interest-only mortgage by approximately 0.09 times a
standard deviation in the first three columns, and by 0.04 of a standard deviation for
the variable rate mortgages. For House value to income, the effect is smaller but still
strongly significant in all regressions. These results are similar to what is reported by
Cocco (2013) for the United Kingdom.17
Overall, interest-only mortgages in Denmark are used prominently across the income,
wealth and age distribution. There is some initial evidence that these products are used
by households that ex-ante were more credit constrained. Moreover, house value and
mortgage size are strong predictors of choosing an IO mortgage, which is consistent
with IO mortgages being more valuable if the reduction in amortization payments
relative to income is larger.
17
All results are robust to using only observations from the years after the reform.
16Table 2: Determinants of Mortgage Choice
House Value to Income Loan to Income
(1) (2) (3) (4) (5) (6) (7) (8)
All Years Controls Fixed Variable All Years Controls Fixed Variable
House value to 0.065*** 0.030*** 0.023*** 0.019***
income (0.000) (0.000) (0.001) (0.000)
Loan size to 0.098*** 0.081*** 0.094*** 0.040***
income (0.000) (0.000) (0.001) (0.000)
Controls No Yes Yes Yes No Yes Yes Yes
Observations 1,529,731 1,528,363 735,565 792,798 1,553,679 1,552,259 744,632 807,627
Notes: The dependent variable is a dummy equal to one if the individuals holds an IO mortgage in 2009. Demographic
controls include age and age squared, years of education, dummies for family size, dummy for female, employment ratio
during the year, an entrepreneur dummy, and a dummy for unemployed. We also include dummies for municipalities
and year of origination. House value to income is the sum of adjusted property values divided by disposable income.
Loan value to income is the mortgage loan size divided by disposable income. House value to income and Loan value
to income are standardized to have zero mean and unit variance. In columns marked by Fixed and Variable we divide
the sample according the interest-rate type. *, **, *** denote statistical significance at the 5%, 1% and 0.1% level.
Regression coefficients estimated with OLS. Robust standard errors in parentheses.
4 Conceptual Framework
How should household consumption respond to a relaxation of borrowing constraints
through an IO mortgage? In this section we consider this question through the lens
of an existing homeowner (which corresponds to our empirical framework). A useful
starting point is that a household that is borrowing unconstrained is by definition
already consuming optimally, meaning that the consumption level is a function of
life-time resources, as in Friedman (1957). An unconstrained household can set a
desired consumption path, borrow when current resources are low relative to lifetime
resources and pay down debt when current resources are high relative to permanent
resources.18 Absent any shocks a relaxation of borrowing constraints through an IO
mortgage should not affect consumption, as the household already could borrow and
consumed optimally by design.19
For a relaxation of borrowing constraints to affect consumption the household needs to
be constrained in her borrowing. Since constraints imply that consumption is below
18
In a model of consumption with an amortization requirement, Svensson (2016) shows that al-
though consumption remain constant with higher amortization payments, borrowing may actually
increase for unconstrained households, as long as the interest rate for borrowing rate is equal to
the interest rate on savings. This is because households borrow more to compensate for the higher
amortization payments.
19
We are abstracting from precautionary savings here, which may be reduced if credit becomes
more readily available. In our empirical results we will investigate this channel more closely.
17the desired level, a relaxation of borrowing constraints induces higher consumption
through higher borrowing. The typical way of modeling this in the macroeconomic
literature has been to relax loan-to-value constraints, where borrowing is constrained
by collateral values (see Guerrieri and Uhlig, 2016, for a comprehensive overview). A
loan-to-value constraint allows the household to borrow an amount M up to a fraction
θH of house value H:
M ≤ θH H
Relaxing this constraint involves either a higher collateral value H or a higher LTV
ratio θH . If the household only faces this constraint, an interest-only mortgage will
not affect borrowing, simply because amortization payments are not in the constraint.
Recent models have instead turned towards payment-to-income constraints, where bor-
rowing is limited by mortgage payments Greenwald (2017); Grodecka (2017); Kaplan
et al. (2017). A PTI constraint limits borrowing by restricting interest payment rm
and amortization payments γ to a fraction θY of income Y :
M (γ + rm ) ≤ θY Y (1)
Relaxing this constraint involves either a higher PTI limit θY , higher income, or lower
mortgage payments. While the focus has mainly been on lower interest payments
(Greenwald, 2017, and a higher PTI limit, see e.g.), lower amortization payments with
this constraint has the same effect. For instance, a household with a mortgage interest
rate of 5 percent and a 3 percent amortization rate that wishes to keep mortgage
payments below 20 percent of income is limited to borrowing at most 2.5 times her
current income. If amortization payments were removed, borrowing can increase to 4
times income.20
We therefore have that for a constrained household, an interest-only mortgage increases
borrowing if the PTI constraint is binding, but not if the LTV constraint is binding.
20
Borrowing to income in the initial example is equal to 0.20/(0.05 + 0.03) = 2.5. With lower
amortization payments, the borrowing capacity is equal to 0.20/0.05 = 4 times income.
18The key question is then to decide what constraint is active: if we want to understand
how IO mortgages affect borrowing and consumption, we need to understand who is
constrained by their mortgage payments. We can rewrite the above constraints as:
θY Y
M̄ ltv = θH H and M̄ pti = ,
(γ + rm )
where M̄ ltv and M̄ pti denote the maximum borrowing given the LTV and PTI con-
straint, respectively. For a borrower who has to fulfill both constraint simultaneously,
the minimum of these two terms will determine borrowing. We can use this intuition
to write the overall debt limit M̄ as:
M̄ = min(M̄ ltv , M̄ pti ).
Since household borrowing capacity is subject to both constraints simultaneously, max-
imum borrowing capacity is determined by the lower of the constraints. In other words,
the PTI constraint will be binding if M̄ pti < M̄ ltv , or:
θY Y
< θH H.
(γ + rm )
Rearranging, we arrive at an expression for when the PTI constraint is binding:
H θY 1
> (2)
Y γ + rm θH
The above equation tells us that if a household is facing financial constraints, the
PTI constraint will be binding for sufficiently high values of H/Y . Note that for a
household facing a PTI constraint, interest rates and amortization payments are func-
tionally equivalent. In this sense, amortization payments represent a real constraint
on borrowing, even though they are fundamentally not a cost but a form of savings.
Intuitively, for sufficiently H/Y , the payments for borrowing are binding, not the
value of the collateral. Even if collateral values are high enough that the LTV con-
straint is not binding, the household is unable to take advantage and cannot borrow
19more. Conversely, if H/Y is sufficiently low, lower mortgage payments will not affect
borrowing.
We illustrate this result in Figure 3, where we plot borrowing according to each con-
straint in panel (a) and the maximum borrowing in panel (b). Both house values and
borrowing are scaled by income. Following the institutional framework in Denmark,
we set θH to 80 percent of house values, and θY to 20 percent of income.21 The LTV
constraint implies that maximum borrowing is linear in collateral values – as the house
value to income ratio increases, so does maximum borrowing. This is represented by
the blue line, where the slope is equal to θH . The PTI constraints is irrespective of the
value of the collateral – the red dashed line denoting the PTI constraint is constant
over H/Y . With an interest rate of 7 percent and amortization payments of 3 percent,
maximum borrowing is equal to 2 times income.
In (b) we plot maximum borrowing according to each constraint, where the constraint
switches from the LTV constraint to the PTI constraint at the threshold in equation
(2). For all values of H/Y above 2.5, the PTI constraint is binding.22 This is indicated
by the dashed vertical line in both figures. Intuitively, while the collateral values are
sufficient to meet the LTV constraint, the payment on any borrowing above this level
will not satisfy the PTI constraint. Conversely, for H/Y below 2.5, the collateral
constraint is binding and the household can only borrow 80 percent of the collateral
values, even though the PTI constraint is slack.
This implies that the household is not fully using her collateral above value of H/Y
above 2.5. IN additoin, this means that leverage (borrowing divided by house value)
is declining in H/Y . As the PTI constraint becomes binding, the household is unable
to borrow against collateral and leverage falls.
What would happen with borrowing if we introduced interest-only mortgages with
these two constraints? In Figure 4 we plot the change in borrowing as we set amor-
21
Formally, there is no PTI constraint in the Danish institutional framework, although mortgage
banks seem to enforce this constraint if we examine the data. The LTV constraint is set by law.
22
We have that the PTI constraint is binding if H/Y is greater than 0.2/(0.07 + 0.03) × 1/0.8 = 2.5.
20Figure 3: Borrowing under Two Constraints
6 .8
6
5
5
Borrowing To Income
Borrowing To Income
4 .6
4
leverage
3
3
2 2 .4
1 1
0 0 .2
0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8
House Value to Income House Value to Income
LTV Constraint PTI Constraint Maximum Borrowing Leverage
(a) Borrowing with a PTI and LTV Constraint (b) Maximum Borrowing and Leverage
Notes: We set the interest rate to 7 percent and amortization payments to 3 percent,. We set the LTV constraint θH
equal to 0.8 and the PTI constraint θY equal to 0.2. Both house values and borrowing are divided by income.
tization payments to zero, thereby increasing the maximum borrowing capacity of
households constrained by the PTI constraint. This correspond to a shift up of the
red dashed line. For values of H/Y below 2.5 times income, borrowing does not change.
For these households, removing amortization payments has no impact on borrowing.
For values above 2.5, however, borrowing increases. For certain house values to in-
come, the binding constraints switch from PTI to LTV, creating an angled upward
slope of the red dashed line. The increase in borrowing is therefore increasing in H/Y ,
although the effect is non-linear in three sections of the H/Y distribution: (1) zero
when the LTV constraint is binding; (2) equal to the borrowing constraint on the LTV
ratio between the new and old threshold values due to a constraint switching effect;
and (3) equal to the increase in the PTI limit if the LTV constraint does not start
to bind. The switch from the PTI constraint to the LTV constraint in the second
section of the H/Y distribution is emphasized in Greenwald (2017), and implies that
certain households are not able to take full advantage of the potential increase in bor-
rowing. Moreover, only households with values above the new threshold can take full
advantage.
In Figure 11 in the appendix we examine how borrowing would change if we instead
change the LTV ratio. Borrowing increases if the LTV constraint is binding, but the
21Figure 4: Borrowing under Two Constraints
6 1
5
.8
Borrowing To Income
Borrowing To Income
4
.6
3
2 .4
1
.2
0
0 1 2 3 4 5 6 7 8 0
House Value to Income 0 1 2 3 4 5 6 7 8
House Value to Income
LTV Constraint New LTV Constraint
PTI Constraint New PTI Constraint Leverage Leverage with new PTI
(a) Maximm (b) Maximum Borrowing and Leverage
Notes: The interest rate is 6 percent and amortization payments are 2 percent of mortgage debt, and the collateral
constraint, θH , is equal to 0.8 and is the slope of the LTV constraint. Both house values and borrowing are divided by
income.
higher maximum LTV ratio also makes the PTI constraint tighter. Effectively, this
result arises because the borrower is able to borrow more against the collateral, which
means that the PTI constraint becomes binding earlier.
Although simple, the conceptual framework illustrates key points for how IO mort-
gages will affect consumption among constrained households. First, IO mortgages
can have a large impact on borrowing and through that channel on consumption for
households that are constrained. Functionally, amortization payments have the same
impact on borrowing as interest rates, as they both enter the payment-to-income con-
straint directly. Although amortization payments are not strictly a cost, they can be
a constraint. If we further believe that not consuming optimally represents a utility
cost, as indeed our consumption models imply, amortization payments reduce utility
directly. In that sense, amortization payments are a utility cost.
Second, Beraja et al. (2018) document that households with higher equity respond
more strongly to a decrease in the interest-rate. The authors argue that with higher
equity, a borrower can not only reduce her costs but also borrow more in response
to an interest-rate cut, which implies that the regional distribution of home equity
is important for monetary policy transmission. In their theoretical model the differ-
ences in the equity distribution occurs because of refinancing incentives, which in turn
22generate convexities in the response to interest rates. In our setup, such convexity
occurs because of constraint switching effects – lower interest rates are most valuable
for households with high H/Y because of the PTI constraint, and those households
also have higher equity (as Figure 3 shows, leverage, which is directly analogous to
equity, is declining in H/Y ).
4.1 Empirical support for two borrowing constraints
The simple framework above has clear predictions that are validated in the data. First,
if IO mortgages are able to relax the binding PTI constraint and if this constraint is
indeed related to H/Y , IO mortgages would be increasing in H/Y . This is indeed what
we find in the data – panel (a) in Figure 5 shows that the house value to income ratio
strongly predicts IO mortgage use. The figure plots the loan share against the house
value to income ratio measured in 2002, showing a strong positive correlation between
IO mortgage share and house value to income ratio for binned bivariate averages,
or “binscatters”.23 Second, the figure shows that consumption to disposable income
ratio is increasing in house value to income ratios. Effectively, this implies that the
consumption rate is higher for households with a high house value to income ratio,
which we take as evidence that these borrowers are more likely to be constrained. The
higher spread around the line in panel b) indicates that there is more variation within
each bin, showing that there is heterogeneity in consumption to disposable income
across house value to income ratios.
Third, we plot leverage over H/Y in panel c). This pattern is consistent with binding
payment-to-income constraints interacting with collateral constraints as in Figure 3.
Borrowers with high house value to income ratios who face two constraints are unable
to borrow against their home equity, and thus leverage is lower.
23
The results are robust to excluding any controls and to focusing on mortgage originated between
2004 and 2006, if we use loan size at origination or loan-to-income values, if we focus only on mortgage
originated in the housing boom, if we use municipality-level data, if we split the sample into households
aged below 40 and above 40, and if we focus on the sample that we use in the estimation.
23Figure 5: House Value to Income and Key Outcomes
.8
1.04
Consumption to disposable income
.7
1.02
IO Loan Share
.6
1
.5 .98
.4 .96
0 2 4 6 8 10 0 2 4 6 8 10
House Value to Income Housing Wealth to Income
(a) IO Loan Share (b) Consumption to Income
1 .35
.3
Interest Payments to Income
.8
.25
Leverage
.6
.2
.4 .15
.1
.2
0 2 4 6 8 10 0 2 4 6 8 10
House Value to Income House Value to Income
(c) Leverage (d) Interest Payments to Income
Notes: The figure plots key outcome variables against the house value to income ratio. House value to income ratio is
the adjusted tax assessed house values divided by disposable income. Panel (a) plots the IO mortgage share against
house values to income. IO mortgage share is calculated using the data from 2009. Panel (b) plots interest-payments
to income against house values to income. Interest-payments to income is the total interest payments divided by
disposable income. Panel (c) plots leverage against house value to income, where leverage is defined as the loan value
divided by total house values. Panel (d) plots consumption to disposable income against house value to income, where
consumption is defined is Section 3. All bins control for year of origination and municipality fixed effects.
24Finally, the conceptual framework predicts that interest-payments are increasing in
H/Y (see Figure 12 in the appendix), but that the curve becomes flat as the borrower
hits the PTI constraint. The figure in panel d) does not fully support this prediction,
instead showing that interest payments to income continues to increase with house
value to income ratios. However, panel a) shows that the IO mortgage share is also
increasing in H/Y . If borrowers can substitute amortization payments for interest-
payments, interest-payments to income continue to increase in H/Y , albeit at a slower
pace. This is indeed what the figure shows. A regression analysis (not reported here)
confirms that the coefficient on H/Y is smaller for values of H/Y higher than 4. The
difference in the coefficients is statistically significant.
Overall, a framework with both a PTI and a LTV constraint generates clear predictions
for borrowing that correspond well to the data. Although the framework is simple,
borrowers appear to act as the theory suggests: borrowing seems to be constrained by
mortgage payments and loan-to-value ratios simultaneously.
5 The Impact of IO Mortgages on Consumption
Expenditure
We use two different methodologies to estimate the impact of IO mortgages on con-
sumption and borrowing. Because we cannot perfectly observe who holds an IO mort-
gage and since this decision may be correlated with other variables that drive consump-
tion growth, we begin with a strategy that leverages an ex-ante measure of exposure
to IO mortgages in an intent-to-treat analysis.
5.1 Empirical Strategy
Our exposure measure follows the intuition developed in the conceptual framework
to estimate the effect of relaxed borrowing constraints on consumption expenditure.
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